High School

When you fold a piece of paper in half, the thickness of the folded piece is twice the thickness of the original piece. A piece of copy paper is about 0.1 mm thick.

**Part 1**
How thick is a piece of copy paper that has been folded in half 7 times?

The piece of paper is about **1.28 cm** thick after being folded 7 times.

**Part 2**
Suppose that you could fold a piece of copy paper in half 12 times. How thick would it be? Write your answer in centimeters.

The piece of paper is about ___ cm thick after being folded 12 times.

Answer :

The theoretical thickness of the piece of paper is not achievable in reality.

What is the geometry of a piece of paper?

The geometry of a piece of paper is a two-dimensional flat shape that can be described as a rectangle or square.

In geometry, a rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides that are equal in length.

A square is a special case of a rectangle, where all four sides are equal in length.

We have,

It's important to note that it is not possible to fold a piece of paper in half more than about 7-8 times due to the physical limitations of the paper's size and thickness.

However, we can still calculate the theoretical thickness of a piece of copy paper that has been folded 12 times.

Part 1:

When a piece of paper is folded in half once, the thickness doubles, so the thickness after one fold is:

0.1 mm x 2 = 0.2 mm

After the second fold, the thickness doubles again:

0.2 mm x 2 = 0.4 mm

We can see that with each fold, the thickness doubles.

So after 7 folds, the thickness would be:

0.1 mm x [tex]2^7[/tex] = 12.8 mm

Converting to centimeters, we get:

12.8 mm = 1.28 cm

Part 2:

Using the same doubling logic, we can find the theoretical thickness of a piece of paper folded 12 times:

0.1 mm x [tex]2^{12}[/tex] = 40.96 mm

Converting to centimeters, we get:

40.96 mm = 4.096 cm

However, as mentioned earlier, it is not possible to fold a piece of paper in half more than about 7-8 times due to physical limitations.

So this theoretical thickness is not achievable in reality.

Thus,

The theoretical thickness of the piece of paper is not achievable in reality.

Learn more about geometry of paper here:

https://brainly.com/question/30739137

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Final answer:

When folded in half 12 times, a piece of copy paper would be approximately 20.48 cm thick.

Explanation:

Part 1: When a piece of copy paper is folded in half 7 times, the thickness doubles each time, resulting in a thickness of [tex]0.1 mm x 2^7 = 1.28 mm (or 1.28 cm).[/tex]

Part 2: If the same paper is folded 12 times, the thickness would be [tex]0.1 mm x 2^12 = 204.8 mm (or 20.48 cm)[/tex].

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